MOTION OF A PAETICLE 133
Integrating we have
or v — = ec-e~*k\
k
Let v = VQ when s = 0, then ec = v<? - . Therefore
Therefore the limiting velocity is V f • In other words, for
A/
large values of s the distance traversed approximately equals
PROBLEMS.
1. A man finds that the resistance of the air to a body moving at the rate of 20 -r—'• equals 1000 dynes per square centimeter of the resisting surface. If 600 -^ is the limit of the velocity with which he can safely land,
find the smallest parachute with which he can safely descend from any height. The man and his parachute have a mass of 75 kg. Take the resistance to be proportional to the velocity.
2. In the preceding problem take the resistance to be proportional to the square of the velocity.
3. Discuss the equation of motion of a boat in still water, after the man who was rowing ships his oars. Suppose the resistance to be proportional to the velocity.
4. A particle is projected with a velocity v in a resisting medium and is acted upon by no other force except that due to the resistance of the medium. Show that, (a) the particle will describe a finite distance in an infinite time when the resistance is proportional to the velocity; (b) it will describe infinite distance in infinite time when the resistance is proportional to the square of the velocity.
6. A bullet is projected vertically upwards with a velocity 00. Supposing the resistance of the air to be proportional to the square of the